Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#14581716 | C2 | semidirect |
| 5. #19127464 | C2 | semidirect |
| 6. #19127463 | C2 | semidirect |
| 7. C2×#103×C83 | C2 | semidirect |
| 12. #14581768 | C4 | semidirect |
| 44. C4⋊Dic83 | C2×C4 | semidirect |
| 54. C2×Q8×C83 | C2×C4 | semidirect |
| 116. C2×D83 | #103 | semidirect |
| 135. C83 | #1872 | semidirect |
| 139. C2×#103 | D83 | semidirect |
| 167. C2×Q8 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581768 | 2 |
| C2×C4⋊C4×D83 | 2 |
| C2×#14581716 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| #19127464 | 2 |
| #19127463 | 2 |
| C2×#103×C83 | 2 |
| #1872 | 83 |